Group rings with solvable unit groups of minimal derived length.

DOI10.1007/s10468-013-9461-8zbMath1309.16025OpenAlexW2004534313MaRDI QIDQ471771

Ernesto Spinelli, Sudarshan K. Sehgal, Gregory T. Lee

Publication date: 17 November 2014

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-013-9461-8

zbMATH Keywords

group ringsunit groupsmodular group algebrasderived lengths

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Derived series, central series, and generalizations for groups (20F14) Units, groups of units (associative rings and algebras) (16U60)

Related Items (3)

On the lower bound of the derived length of the unit group of a nontorsion group algebra ⋮ Modular group algebras with centrally metabelian unit groups ⋮ Group rings with metabelian unit groups

Cites Work

• Unnamed Item
• Meta-abelian unit groups of group algebras are usually abelian
• Group identities on units and symmetric units of group rings.
• GROUP ALGEBRAS WITH UNIT GROUPS OF DERIVED LENGTH THREE
• On the derived length of the unit group of a group algebra
• Group algebras whose units satisfy a group identity. II
• A NOTE ON THE DERIVED LENGTH OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA
• ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA
• On the Solvability of Unit Groups of Group Algebras
• Lie Solvable Group Rings
• Group Algebras with a Solvable Group of Units^#

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